SCC Malaria Research Team

2009-05-15 22:14 by Ian

My research team was in the news!
Scottsdale Community College – SCC Students Present Research Project at ASU Symposium

2019.08.08: Update

I found a bunch of my old notes while scanning papers from school. Figured I’d post them for the benefit of some discussions I’ve had recently on mathematical models. To that end, I will give some brief narrative surrounding the material. I will add more if/when I find it.

Here is the Malaria UBM Outline as put together by Dr. Nagy.

Before you can model a complex dynamic system, you have to give some careful thought to the thing in the world you are trying to model. It’s one thing to model a system that is already well-understood (as would be the case in most undergraduate physics courses). These are often cases where you want to figure out how much of what things you need to produce a given amount of something. But the model can be written from existing knowledge.

It is an entirely different thing for systems whose workings are not fully clear, or even unknown (climates, turbulence, neutron stars, and the interiors of living things). This model is the latter case; using a mathematical model to tease out things to look for in the real world. Since we shouldn’t intentionally infect people with diseases for the sake of understanding them, and since it’s too expensive or impossible to fully analyze many incidental cases to test the hypothesis, we build a mathematical model that represents our hypothesis and test it against conditions that we might plausibly find in the real world. If the model generates good predictions, it shortens the route to knowledge for experimentalists to find plausible causes for things in the real world.

Our research director, Dr. Nagy, found a hypothesis that was recently published which he believed merited attention. He wanted help refining and testing. He, myself and Michael Crusoe argued back and forth and at one point, made an initial (simple) toy model (not further discussed here) to see if the hypothesis was even feasible against idle attack. It passed, and we proceeded to spend the time to refine the hypothesis. Both for the sake of adding factors that we wanted initially, but were difficult to add, and for addressing weaknesses we found in the initial model. Here are some of my hand-written notes from a meeting near this time.
Malaria notes intro

After lots of hard work reading existing literature and discussion, this is a schematic of the refined hypothesis that we put together in preparation for modeling:

Malaria flowchart
This was drawn by my hand (because I suspect Michael liked how neatly I render things like this), but the idea represented was developed by the team from reading the papers posted below (among others).

Once we agreed on what we thought actually kills people and how it kills them we started a hard grind on representing the idea in a system of differential equations.

Here are some notes I took from a meeting where we were discussing specifics about the model.
Model notes, sheet 0

Model notes, sheet 1

It’s been awhile since I’ve looked at any of this stuff, but I think this DFE analysis was M. Crusoe’s work.

Here are my notes to my teammates who had made changes to the model that I was asked to help scrutinize and document for others. I won’t assume my reader has Maple installed, so here is a PDF render of the Maple sheet.

One of my teammates put together this nice overview of our model. And another turned our work into a presentation of our thesis.

The final draft of the poster used at the symposium.

Papers we used to inform our hypothesis, tune free parameters, or otherwise influenced our thinking

Mouse-over text are my notes on the value of the paper to our research efforts. There are still papers I haven’t dug out of the ice, but this is a good start.